A robust implicit state observer for multiple-input multiple-output uncertain systems

A new mathematical method of estimating the state for uncertain continuous-time multiple-input multiple-output minimum-phase (with respect to the relation between the disturbance and the output) dynamical systems with arbitrarily relative degrees is presented. For the systems with relative degree one, the state observer which is perfectly robust to disturbances is constructed by using only the input and output information. The estimating error of the state decays to zero exponentially. For the systems with higher relative degrees, the state observer is formulated for the first time, where the input and output information, and the a priori information of the upper and lower bounds of the disturbances are employed. In this case, the estimating error of the state can be controlled to be as small as is needed by the design parameters. The attraction of the proposed observers lies in their robustness to disturbances and insensitivity to the high-frequency noises accompanying the inputs. A design example and its simulation results are presented to illustrate the proposed algorithm.